One of the consequences is that doctors are beholden to large corporations who have teams of lawyers to handle legal issues and malpractice lawsuits. Since there are limited slots, some of them even work in foreign countries until they get experience to land a job in the US, which is a waste of talent.
If anyone could start a medical practice, a new syringe company could sell to smaller practices that haven't yet been mired in enterprise contracts.
Right now, in order to even build a hospital you have to submit "evidence of need" to the government to get approval. Imagine if every startup had to convince a bureaucrat that they were needed: fewer people would be interested in starting one.
It's probably worth considering moving medical negotiations from insurance companies and employers to the consumer. I don't know that it's very common to call up multiple doctors and find the one with the lowest price, because you're paying your insurance company to do the negotiation for you. Taxing employer-provided health insurance as income might remove the incentive for them to provide it at all. Together with deregulating the entire medical industry, it would make it possible to buy cheap treatment without insurance, which might be enough to make insurance less important.